So basically, an alpha channel is just a greyscale image that is used to represent transparency. Not all softwares have the same interpretation, but in Photoshop, black is fully transparent and white is fully opaque. The various shades of grey between black and white become different degrees of semi-transparent. Sometimes you have to invert your alpha as some softwares will assume white as transparent and black as opaque.

Some image formats can hold this greyscale alpha image as well as the regular rgb image that you are saving out. This means that if you need to maintain transparency information for use in a 3d package, you have all that information in the image.

So how do you create on in photoshop? There are a few ways, but probably the easiest is to load the element as a selection, go into the channels tab, and create a new channel. In this new channel, fill the selection with white. This will maintain semi transparency too. When you save out now, you file will have an alpha, providing you are using a format that can hold alpha information. The most common of these are:
.tif, .tga, .exr, and i think .png and a couple of others. A quick google search will tell you all of them if you need them.